Перевести в косвенную речь: The doctor said "Pete, are you coughing

The doctor said "Pete, are you coughing badly?" The doctor asked Pete if he was coughing badly.

When we turn direct speech into indirect speech we make some changes. We change said into asked. We change the second person into the third person singular (you he) due to the first part of the sentence. We put if as the second part of the sentence is general question and there is no interrogative word. We change the tense of the second part of the sentence. We change Present Continuous into Past Continuous.